In the systems I've been involved with:
- Software - Open Source - not just the Electoral Commission has access to it, it's published on the web for anyone to verify. Operating system and compiler are also open-source.
- Spot-Checking - Conducted by the Electoral Commission, who may invite 3rd parties such as Universities to check.
- Background Checking - all those involved held security clearances at various levels.
- Equipment Certification - Commercial Off-The-Shelf Hardware is used - and certified by the Electoral Commission
- Dispute Resolution - handled by using alternate paper ballots, with Electoral Commission quarantining hardware for 3rd party inspection. In theory. as far as I know, there's been no disputes.